Unlocking Interpretability for RF Sensing: A Complex-Valued White-Box Transformer

The empirical success of deep learning has spurred its application to the radio-frequency (RF) domain, leading to significant advances in Deep Wireless Sensing (DWS). However, most existing DWS models function as black boxes with limited interpretability, which hampers their generalizability and raises concerns in security-sensitive physical applications. In this work, inspired by the remarkable advances of white-box transformers, we present RF-CRATE, the first mathematically interpretable deep network architecture for RF sensing, grounded in the principles of complex sparse rate reduction. To accommodate the unique RF signals, we conduct non-trivial theoretical derivations that extend the original real-valued white-box transformer to the complex domain. By leveraging the CR-Calculus framework, we successfully construct a fully complex-valued white-box transformer with theoretically derived self-attention and residual multi-layer perceptron modules. Furthermore, to improve the model's ability to extract discriminative features from limited wireless data, we introduce Subspace Regularization, a novel regularization strategy that enhances feature diversity, resulting in an average performance improvement of 19.98% across multiple sensing tasks. We extensively evaluate RF-CRATE against seven baselines with multiple public and self-collected datasets involving different RF signals. The results show that RF-CRATE achieves performance on par with thoroughly engineered black-box models, while offering full mathematical interpretability. More importantly, by extending CRATE to the complex domain, RF-CRATE yields substantial improvements, achieving an average classification gain of 5.08% and reducing regression error by 10.34% across diverse sensing tasks compared to CRATE. RF-CRATE is fully open-sourced at: https://github.com/rfcrate/RF_CRATE.